Suppose that ?!,···, ?" form a random sample from the beta distribution with parameters ? and...

Suppose that ?!,···, ?" form a random sample from the beta distribution with parameters ? and
?. Find the moments estimators for ? and ?.

NOTE: Please make the solution as well detailed as possible especially the making of ? and
? the subject of formular respectively

Expert Solution

orchestra answered 1 year ago

We observe a random sample of n values from the beta distribution with parameters c and...

We observe a random sample of n values from the beta distribution with parameters c and 2. (a) Find a general expression for the method of moments (MOM) estimate of c, and calculate this MOM estimate for the case where we observe two values, 0.96 and 0.84. (b) Find the bias of the MOM estimator of c for the case where c = 1 and n = 1. (c) Find a general expression for the maximum likelihood estimate (MLE) of...

Suppose that X1, ..., Xn form a random sample from a uniform distribution for on the...

Suppose that X1, ..., Xn form a random sample from a uniform distribution for on the interval [0, θ]. Show that T = max(X1, ..., Xn) is a sufficient statistic for θ.

Let Xl, n be a random sample from a gamma distribution with parameters a = 2...

Let Xl, n be a random sample from a gamma distribution with parameters a = 2 and p = 20. a) Find an estimator , using the method of maximum likelihood b) Is the estimator obtained in part a) is unbiased and consistent estimator for the parameter 0? c) Using the factorization theorem, show that the estimator found in part a) is a sufficient estimator of 0.

Suppose that X1,X2,...,Xn form a random sample from a uniform distribution on the interval [θ1,θ2], where...

Suppose that X1,X2,...,Xn form a random sample from a uniform distribution on the interval [θ1,θ2], where (−∞ < θ1 < θ2 < ∞). Find MME for both θ1 and θ2.

Suppose X1, X2, , ... , X10is a random sample from a distribution with mean u...

Suppose X1, X2, , ... , X10is a random sample from a distribution with mean u and variance 6. Also, is a random sample from a distribution with mean u and variance 30. These samples are independent as well. a. Is 0.2X + 0.8Y unbiased? Cannot be determined from this information or Yes or No b. What is the MSE of u? Round to 2 decimals. c. Based on the MSE criterion, is mu (u ), X (x bar), or Y (y...

Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2) distribution,...

Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2) distribution, where μ is unknown but σ2 is known, and it is of interest to test H0: μ = μ0 versus H1: μ ̸= μ0 for some value μ0. The R code below plots the power curve of the test Reject H0 iff |√n(X ̄n − μ0)/σ| > zα/2 for user-selected values of μ0, n, σ, and α. For a sequence of values of μ,...

Suppose we wish to generate a sample from the exponential ($\beta$) distribution, and only have access...

Suppose we wish to generate a sample from the exponential ($\beta$) distribution, and only have access to a computer which generates numbers from the skew logistic distribution. It turns out that if $X$~SkewLogistic ($\beta$), then log(1+exp($-X$)) is exponential ($\beta$). Show that this is true and check by simulation that this transformation is correct.

X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution....

X ~ N (60, 9). Suppose that you form random samples of 25 from this distribution. Let X−be the random variable of averages. Let ΣX be the random variable of sums. To make you easy, drawing the graph, shade the region, label and scale the horizontal axis for X− and find the probability. X−~ N (60, 9/ 25) 9) P (X−< 60) = _____ a. 0.4 b. 0.5 c. 0.6 d. 0.7 10) Find the 30th percentile for the mean. a. 0.56...

Let X1…X5 be iid random sample of size n=5 from a Uniform distribution with parameters 0,theta....

Let X1…X5 be iid random sample of size n=5 from a Uniform distribution with parameters 0,theta. We test H0: theta=1 versus H1: theta=2. Reject H0 when max(X1…X5)>b. Find the value of b so that the size of the test is 0.10, then find the power of this test. Among the tests based on max(X1…Xn), find the most powerful test with size exactly equal to 0.

e. Suppose a random sample of size 100 is taken from a distribution with mean 200...

e. Suppose a random sample of size 100 is taken from a distribution with mean 200 and variance 400. What is the distribution of the sample mean ?%? (State the name and parameter(s) of the distribution) f. For a medical test, the probability of testing positive for a healthy person is 5%. Based on this, can we find the probability of testing positive for an infected person? If yes, explain how; if no, explain why.

Question